Linked bibliography for the SEP article "Frege’s Theorem and Foundations for Arithmetic" by Edward N. Zalta
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Primary Literature
Cited Works by Frege
- 1879, Begriffsschrift, eine der arithmetischen nachgebildete
Formelsprache des reinen Denkens, Halle a. S.: Louis Nebert;
translation by S. Bauer Mengelberg as Concept Notation: A formula
language of pure thought, modelled upon that of arithmetic, in J.
van Heijenoort, From Frege to Gödel: A Sourcebook in
Mathematical Logic, 1879–1931, Cambridge, MA: Harvard
University Press
- 1884, Die Grundlagen der Arithmetik: eine
logisch-mathematische Untersuchung über den Begriff der
Zahl, Breslau: w. Koebner; translated by J. L. Austin as The
Foundations of Arithmetic: A Logic-Mathematical Enquiry into the
Concept of Number, Oxford: Blackwell, second revised edition,
1953.
- 1892, “Über Begriff und Gegenstand”, in
Vierteljahresschrift für wissenschaftliche Philosophie,
16: 192–205; translated as ‘Concept and Object,’ by
P. Geach in Translations from the Philosophical Writings of
Gottlob Frege, P. Geach and M. Black (eds. and trans.), Oxford:
Blackwell, third edition, 1980. (Scholar)
- 1893/1903, Grundgesetze der Arithmetik, Band I/II, Jena:
Verlag Herman Pohle; translation by P. Ebert and M. Rossberg (with C.
Wright) as Basic Laws of Arithmetic: Derived using
concept-script, Oxford: Oxford University Press, 2013; partial
translation of Volume I by M. Furth as The Basic Laws of
Arithmetic, Berkeley: U. California Press, 1964. (Scholar)
- 1953, The Foundations of Arithmetic, J. L. Austin
(trans.), Oxford: Basil Blackwell, 2nd revised edition.
- 1967, The Basic Laws of Arithmetic, M. Furth (trans.),
Berkeley: University of California.
- 1980, Philosophical and Mathematical Correspondence, G.
Gabriel, H. Hermes, F. Kambartel, C. Thiel, and A. Veraart (eds. of
the German edition), abridged from the German edition by Brian
McGuinness, translated by Hans Kaal, Chicago: University of Chicago
Press.
Cited Primary Works by Others
- Dedekind, R., 1888, Was sind und was sollen die Zahlen, Braunschweig: Vieweg und Sohn; 2nd edition, 1893; 7th edition, 1939; translated as “The Nature and Meaning of Numbers”, in W.W. Beman (ed. and trans.), Essays on the Theory of Numbers, Chicago: Open Court, 1901; reprinted, New York: Dover, 1963; also translated as “What Are Numbers and What Should They Be?”, H. Pogorzelski, W. Ryan & W. Snyder (eds. and trans.), Orono, ME: Research Institute for Mathematics, 1995. (Scholar)
- Hilbert, D., 1899, “Grundlagen der Geometrie”, in
Festschrift zur Feier der Enthüllung des Gauss-Weber
Denkmals in Göttingen, Leipzig: Teubner; translated as
Foundations of Geometry, Leo Unger (trans.), La Salle: Open
Court, 1971 (ninth printing, 1997). (Scholar)
- Pasch, M., 1882, Vorlesungen über neuere Geometrie,
Leipzig: Teubner. (Scholar)
- Peano, G., 1889a, Arithmetices Principia: Nova Methodo
Exposita, Turin: Fratelli Bocca; translated as “The
Principles of Arithmetic, Presented by a New Method”, in Jean
van Heijenoort (ed.), From Frege to Gödel: A Source Book in
Mathematical Logic, 1879--1931, Cambridge, MA: Harvard University
Press, 1967, 83–97. (Scholar)
- Peano, G., 1889b, I principii di geometria logicamente
esposti, Turin: Fratelli Bocca.
- Pieri, M., 1898, “I principii della geometria di posizione
composti in sistema logico deduttivo”, Memorie della Reale
Accademia delle Scienze di Torino (Series 2), 48: 1–62.
- Whitehead, A.N., and B. Russell, 1910--1913, Principia Mathematica, 3 volumes, Cambridge: Cambridge University Press; 2nd edition, Cambridge: Cambridge University Press, 1925--1927. (Scholar)
Secondary Literature
- Anderson, D., and Zalta, E., 2004, “Frege, Boolos, and Logical Objects”, J. Philosophical Logic, 33 (1): 1–26. (Scholar)
- Antonelli, A., and May, R., 2005, “Frege’s Other Program”, Notre Dame Journal of Formal Logic, 46 (1): 1–17. [Available online in PDF.] (Scholar)
- Beaney, M., 1997, The Frege Reader, Oxford: Blackwell. (Scholar)
- Bell, J. L., 1995, “Type-Reducing Correspondences and
Well-Orderings: Frege’s and Zermelo’s Construction
Re-examined”, Journal of Symbolic Logic, 60:
209–221. (Scholar)
- –––, 1999, “Frege’s Theorem in a
Constructive Setting”, Journal of Symbolic Logic, 64
(2): 486–488. (Scholar)
- –––, 1994, “Fregean Extensions of First-Order Theories”, Mathematical Logic Quarterly, 40: 27–30; reprinted in Demopoulos 1995, 432–437. (Scholar)
- Boolos, G., 1985, “Reading the Begriffsschrift”, Mind, 94: 331–344; reprinted in Boolos (1998): 155–170. [Page references are to the reprint.] (Scholar)
- –––, 1986/87, “Saving Frege From Contradiction”, in Proceedings of the Aristotelian Society, 87(1): 137–151; reprinted in Boolos (1998): 171–182. [Page references are to the original.] (Scholar)
- –––, 1987, “The Consistency of
Frege’s Foundations of Arithmetic”, in On
Being and Saying, J. J. Thomson (ed.), Cambridge, MA: MIT Press,
pp. 3–20; reprinted in Boolos (1998): 183–201. [Page
references are to the original.] (Scholar)
- –––, 1990, “The Standard of Equality of Numbers”, in Meaning and Method: Essays in Honor of Hilary Putnam, G. Boolos (ed.), Cambridge: Cambridge University Press, pp. 261–277; reprinted in Boolos (1998): 202–219. [Page references are to the original.] (Scholar)
- –––, 1993, “Whence the Contradiction?”, in Aristotelian Society Supplementary Volume, 67: 213–233; reprinted in Boolos (1998): 220–236. (Scholar)
- –––, 1994, “The Advantages of Honest Toil
Over Theft”, in Mathematics and Mind, Alexander George
(ed.), Oxford: Oxford University Press, 27–44; reprinted in
Boolos (1998): 255–274. (Scholar)
- –––, 1997, “Is Hume’s Principle
Analytic?”, in Heck (ed.) 1997, 245–262; reprinted in
Boolos (1998): 301–314. [Page references are to the
reprint.] (Scholar)
- –––, 1998, Logic, Logic, and Logic, J. Burgess and R. Jeffrey (eds.), Cambridge, MA: Harvard University Press. (Scholar)
- Burgess, J., 1984, “Review of Wright (1983)”, The
Philosophical Review, 93: 638–40. (Scholar)
- –––, 1998, “On a Consistent Subsystem of
Frege’s Grundgesetze”, Notre Dame Journal of
Formal Logic, 39: 274–278. (Scholar)
- –––, 2005, Fixing Frege, Princeton: Princeton University Press. (Scholar)
- Demopoulos, W., 1998, “The Philosophical Basis of Our Knowledge of Number”, Noûs, 32: 481–503. (Scholar)
- Demopoulos, W., (ed.), 1995, Frege’s Philosophy of Mathematics, Cambridge: Harvard University Press. (Scholar)
- Demopoulos, W., and Clark, P., 2005, “The Logicism of Frege, Dedekind and Russell”, in Oxford Handbook of Philosophy of Mathematics and Logic, S. Shapiro (ed.), Oxford: Oxford University Press, 129–165. (Scholar)
- Dummett, M., 1991, Frege: Philosophy of Mathematics, Cambridge: Harvard University Press. (Scholar)
- –––, 1997, “Neo-Fregeans: In Bad Company?”, in Schirn (1997). (Scholar)
- Ferreira, F., 2005, “Amending Frege’s Grundgesetze
der Arithmetik”, Synthese, 147: 3–19. (Scholar)
- Ferreira, F., and K. Wehmeier, 2002, “On the Consistency of
the \(\Delta^1_1\)-CA Fragment of Frege’s
Grundgesetze”, Journal of Philosophical Logic,
31: 303–311. (Scholar)
- Field, H., 1984, “Critical Notice of Crispin Wright:
Frege’s Conception of Numbers as Objects”,
Canadian Journal of Philosophy, 14: 637–632; reprinted
under the title “Platonism for Cheap? Crispin Wright on
Frege’s Context Principle” in H. Field, Realism,
Mathematics, and Modality, Oxford: Blackwell, 1989, pp.
147–170. (Scholar)
- Fine, K., 2002, The Limits of Abstraction, Oxford: Clarendon Press. (Scholar)
- Furth, M., 1967, “Editor’s Introduction”, in G.
Frege, The Basic Laws of Arithmetic, M. Furth (translator and
editor), Berkeley: University of California Press, pp.
v–lvii. (Scholar)
- Geach, P., 1976, “Critical Notice”, Mind, 85 (339): 436–449. (Scholar)
- –––, 1955, “Class and Concept”, Philosophical Review, 64: 561–570. (Scholar)
- Goldfarb, W., 2001, “First-Order Frege Theory is Undecidable”, Journal of Philosophical Logic, 30: 613–616. (Scholar)
- Hale, B., 1994, “Dummett’s Critique of Wright’s
Attempt to Resuscitate Frege”, Philosophia Mathematica,
(Series III), 2: 122–147. (Scholar)
- Hazen, A., 1985, “Review of Crispin Wright’s
Frege’s Conception of Numbers as Objects”,
Australasian Journal of Philosophy, 63 (2):
251–254. (Scholar)
- Heck, Jr., R., 2012, Reading Frege’s Grundgesetze,
Oxford: Clarendon Press. (Scholar)
- –––, 2011, Frege’s Theorem, Oxford: Clarendon Press. (Scholar)
- –––, 1999, “Grundgesetze der Arithmetik I, §10”, Philosophia Mathematica, 7: 258–292. (Scholar)
- –––, 1997, “The Julius Caesar Objection”, in Heck (ed.) 1997, 273–308. (Scholar)
- –––, 1996, “The Consistency of Predicative
Fragments of Frege’s Grundgesetze der
Arithmetik”, History and Philosophy of Logic, 17:
209–220. (Scholar)
- –––, 1993, “The Development of Arithmetic
in Frege’s Grundgesetze der Arithmetik”,
Journal of Symbolic Logic, 58 (2): 579–600; reprinted
in Demopoulos (1995). (Scholar)
- Heck, R. (ed.), 1997, Language, Thought, and Logic: Essays in Honour of Michael Dummett, Oxford: Oxford University Press, 1997. (Scholar)
- Hodes, H., 1984, “Logicism and the Ontological Commitments of Arithmetic,” Journal of Philosophy, 81 (3): 123–149. (Scholar)
- Linnebo, Ø., 2004, “Predicative Fragments of Frege Arithmetic”, The Bulletin of Symbolic Logic, 10 (2): 153–174. (Scholar)
- MacBride, F., 2003, “Speaking with Shadows: A Study of Neo-Logicism”, British Journal for the Philosophy of Science, 54: 103–163. (Scholar)
- MacFarlane, J., 2002, “Frege, Kant, and the Logic in Logicism”, The Philosophical Review,111:25–65. (Scholar)
- May, R., and K. Wehmeier, 2019, “The Proof of
Hume’ Principle”, P. Ebert and M. Rossberg (eds.), Essays
on Frege’s Basic Laws of Arithmetic, Oxford: Oxford
University Press, pp. 182–206. (Scholar)
- Parsons, C., 1965, “Frege’s Theory of Number”, Philosophy in America, M. Black (ed.), Ithaca: Cornell University Press, pp. 180–203; reprinted with Postscript in Demopoulos (1995), pp. 182–210. (Scholar)
- Parsons, T., 1987, “The Consistency of the First-Order
Portion of Frege’s Logical System”, Notre Dame Journal
of Formal Logic, 28: 161–68. (Scholar)
- Pelletier, F.J., 2001, “Did Frege Believe Frege’s
Principle”, Journal of Logic, Language, and
Information, 10 (1): 87–114. (Scholar)
- Quine, W.V.O., 1995, “On Frege’s Way Out”, in
Selected Logical Papers (enlarged edition), Cambridge, MA:
Harvard University Press. (Scholar)
- Reck, E., and Awodey, S. (trans./eds.), 2004, Frege’s
Lectures on Logic: Carnap’s Student Notes, 1910–1914,
Chicago and La Salle, IL: Open Court. (Scholar)
- Resnik, M., 1980, Frege and the Philosophy of Mathematics, Ithaca: Cornell University Press. (Scholar)
- Rosen, G., 1993, “The Refutation of Nominalism(?)”, Philosophical Topics, 21 (2): 149–186 (Scholar)
- Ruffino, M., 2003, “Why Frege Would Not Be A Neo-Fregean”, Mind, 112 (445): 51–78. (Scholar)
- Schirn, M., (ed.), 1997, Philosophy of Mathematics Today,
Oxford: Oxford University Press. (Scholar)
- Schroeder-Heister, P., 1987, “A model-theoretic
reconstruction of Frege’s Permutation Argument”, Notre
Dame Journal of Formal Logic, 28 (1): 69–79. (Scholar)
- Sullivan, P. and Potter, M., 1997, “Hale on Caesar”, Philosophia Mathematica (Series III), 5: 135–152. (Scholar)
- Tabata, H., 2000, “Frege’s Theorem and His
Logicism”, History and Philosophy of Logic, 21 (4):
265–295. (Scholar)
- Tennant, N., 2004, “A General Theory of Abstraction Operators”, The Philosophical Quarterly, 54(214): 105–133. (Scholar)
- van Heijenoort, J., 1967, ed., From Frege to Gödel: A
Sourcebook in Mathematical Logic, Cambridge: Harvard University
Press.
- Wehmeier, K., 1999, “Consistent Fragments of
Grundgesetze and the Existence of Non-Logical Objects”,
Synthese, 121: 309–328. (Scholar)
- Wright, C., 1983, Frege’s Conception of Numbers as Objects, Aberdeen: Aberdeen University Press. (Scholar)
- –––, 1997a, “Response to Dummett”, in Schirn (1997). (Scholar)
- –––, 1997b, “On the Philosophical
Significance of Frege’s Theorem”, in Heck (ed.) 1997,
201–244. (Scholar)
- Zalta, E., 1999, “Natural Numbers and Natural Cardinals as
Abstract Objects: A Partial Reconstruction of Frege’s
Grundgesetze in Object Theory”, Journal of
Philosophical Logic, 28 (6): 619–660. (Scholar)